To solve the problem, we need to determine the distance traveled per revolution and find the slope of the graph.
(a) To find how many revolutions Melissa makes per foot of distance traveled, we can use the information from the graph provided in your prompt.
From the graph, if we consider the values, we can extract a specific example like:
- At 2 revolutions, she travels 10 feet.
- This means for every 2 revolutions, the distance is 10 feet.
To find the distance traveled per revolution: \[ \text{Distance per revolution} = \frac{\text{Distance traveled}}{\text{Number of revolutions}} \] Using the example above: \[ \text{Distance per revolution} = \frac{10 \text{ feet}}{2 \text{ revolutions}} = 5 \text{ feet/revolution} \] This means Melissa makes 1 revolution for every 5 feet of distance traveled: \[ \text{Revolutions per foot} = \frac{1 \text{ revolution}}{5 \text{ feet}} = 0.2 \text{ revolutions/foot} \] So, Melissa makes 0.2 revolutions per foot of distance traveled.
(b) The slope of the graph represents the rise over run, which in this case is the change in distance traveled per change in revolutions (i.e., how many feet she travels per revolution).
Using the same information from the graph:
- For example, from 0 revolutions to 2 revolutions, the distance increases from 0 feet to 10 feet.
- The change in distance (rise) is \(10 - 0 = 10\) feet.
- The change in revolutions (run) is \(2 - 0 = 2\) revolutions.
Calculating the slope: \[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{10 \text{ feet}}{2 \text{ revolutions}} = 5 \text{ feet/revolution} \]
So, the slope of the graph is 5 feet/revolution.
To summarize:
(a) Melissa makes 0.2 revolutions per foot of distance traveled.
(b) The slope of the graph is 5 feet/revolution.
3 answers